Tom claims that because the data pairs (1, 4), (2, 6), (3, 9), and (4, 13.5) have y-value with a common ratio, they are best modeled by a quadratic function. What is his error?

Is it supposed to be modeled by an exponential function?

yes

thanks

Tom's error is in assuming that the data pairs have a common ratio, indicating a geometric progression. However, the data pairs he provided do not form a geometric progression, as there is no consistent ratio between the y-values.

To determine the best model for the data, it is important to critically analyze the relationship between the x-values and y-values. In this case, the y-values do not exhibit a common ratio, but rather an increasing trend that is not consistent with a quadratic or geometric progression.

Therefore, Tom's error lies in assuming the wrong type of function to model the data. Instead, it would be more appropriate to consider a different type of function, such as an exponential function to better capture the increasing trend in the data.